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CXN: A Case Study

             Carrie Beam                               Gene Fusz
 The Fisher Center for Management,                   President, CXN
    Information and Technology                   925 N. Lindbergh Blvd
      Haas School of Business                     St. Louis, MO 63141
University of California, Berkeley                 genefusz@cxn.com
        Berkeley, CA 94720
      beam@haas.berkeley.edu


                      CMIT Working Paper 97-WP-1025

                              October 14, 1997
Table of Contents


1   Introduction............................................................................................................. 1
2   Background ............................................................................................................. 1
3   Designing the Exchange Environment ..................................................................... 3
  3.1 Starting with the Traditional English Auction ...................................................... 4
  3.2 Departing from the English Auction: Major Differences ..................................... 5
  3.3 Supporting a New Auction with Information Technology .................................... 6
  3.4 Comparing the Traditional English Auction and CXN ......................................... 7
4   Value Added from the Information System.............................................................. 8
5   Conclusions and Areas for Further Research............................................................ 9
6   Appendix............................................................................................................... 10




                                                     List of Tables

Table 1     Initial Sequence of Transactions ...................................................................... 10
Table 2     Seller and Buyer Agree to Close Sale............................................................... 11
Table 3     The Seller Cannot Deliver the Merchandise ..................................................... 12
Table 4     The Buyer Changes His Mind.......................................................................... 12
Abstract

CXN is a startup company which is designing an Internet-based exchange mechanism to
sell new consumer products (such as televisions) in a new and efficient manner. It
introduces a variant of the standard English auction, in which sellers are the bidders and
the single buyer is the auctioneer. CXN uses information technology and the Internet to
depart from standard English auction methodology. Major differences include the
support of asynchronous bidder participation, the continuously running auction, and the
ability to auction off multiple items in a succession of single-item sales. Additionally, the
Internet provides a broader audience and grants some degree of immunity from rings of
bidders.

1   Introduction

This case study outlines the workings of the Consumer Exchange Network, or CXN
(www.cxn.com). CXN is a St. Louis, MO-based startup company with the mission of
providing an efficient online pricing mechanism to bring together buyers and sellers of
new consumer products.

Gene Fusz, the President of CXN, called Carrie Beam of the Fisher Center in the spring
of 1997 to discuss the workings of the new business. This case study has come out of the
collaboration between Gene and Carrie. CXN is currently in beta testing. The site offers
camcorders only at this point in time, and is looking for further funding before it
broadens its offerings.

2   Background

CXN grew out of a desire to bring buyers and sellers of new branded consumer products,
such as televisions and VCRs, together in an efficient manner. Consumer products are
sold on the “Big Board.”

CXN is an Internet-based exchange environment which sells new consumer products
through a patent-pending auction mechanism. Because it provides no warehousing,
transportation, or advertising, it hopes to provide buyers with a more efficient and less
expensive environment than the traditional consumer products superstores, such as Fry’s
Electronics or Best Buy. While business-to-business procurement is certainly not
excluded, CXN currently targets individual buyers and attempts to match them with
corporate sellers. The corporate sellers could include (but are not limited to) current
superstores, importers, and warehouses.

Briefly, this is how CXN works. Both buyers and sellers are anonymous until a sale has
been made, at which time CXN provides the parties the information necessary to
complete the sale.




                                             1
From the seller’s point of view, CXN works as follows. First, seller joins the CXN
network for one-time member registration fee of $25 or less. Second, the seller purchases
an offer posting certificate; the certificate details the type of merchandise offered and the
offering price. The price of the certificate depends on the asking price of the
merchandise being sold, and will be from $1-$10 for products costing from $50 to $1000.
Third, the seller’s offer becomes visible to buyers only if it’s the lowest priced offer. If a
buyer chooses to purchase the seller’s merchandise, CXN will provide each party with
information necessary to contact the other, and the trade is arranged.1

From the buyer’s point of view, CXN works as follows. Buyers must first join the CXN
network by paying a one-time new member registration fee of $25 or less. A buyer
interested in a new color television will then locate the product on the CXN menu. The
buyer will see only the lowest price offered nationwide, a price which was determined by
the auction environment in which several sellers bid against each other.2 The
environment was designed to make the buyer’s experience as simple and easy as possible.
The buyer will then purchase an option for $10, which locks in the price for that product
for one day (8 full business hours). CXN provides the buyer with information necessary
to contact the seller, and the trade is arranged.

A preliminary sellers’ bidding screen design is shown below in Figure 1. This screen is
available only to sellers, and it shows the seller the differing price levels, as well as the
quantity available at each price. Buyers only see the lowest price offered – in this case,
$200 for the television.

                          Figure 1 Preliminary Screen Design
             Sony 19” Color TV Quantity Available     Timestamp
                    $210                  10                 4/2/97
                    $205                  42                3/25/97
                    $200                  35                 4/2/97
                    $200                  4                  4/1/97
                        3
                   $195




1
  To protect buyer privacy, currently CXN provides the buyer’s name and email address only to the seller.
In addition to the seller’s name and email address, the buyer receives the seller’s telephone number, fax
number, company name and address, contact person, and, where appropriate, driving directions.
2
  Currently, shipping costs are not included. They average $10-$20 on a several-hundred-dollar camcorder.
CXN plans to have ZIP code functionality which determines buyer and seller locations and then adds
appropriate shipping costs to the price each buyer sees. Hence, the price an individual buyer sees is the
lowest price, including shipping, available to her; it may or may not reflect the lowest raw price
nationwide. This is an important part of CXN’s offerings; however, in the interests of simplicity this case
study deliberately excludes the ZIP code when formulating the basic model. It assumes instead shipping
and handling costs are the same from all sellers to all buyers. The offering prices on the CXN exchange do
not include sales tax.
3
  There is no current offer at $195; the lowest current offer is $200. The $195 is there to make it more
inviting for the sellers to move down to the next level.


                                                    2
Items are sorted (and hence offered to buyers) first by lowest price, and then by earliest
timestamp. Several sellers may be at each price level; in that case, CXN relies upon
slight differences in timestamp to differentiate them. Each seller may offer a single item
for sale by purchasing a single offer posting certificate. Each seller may also offer an
entire lot of identical items at the same price by purchasing a single offer posting
certificate and choosing the automatic renew feature, to purchase another offer posting
certificate when the first one sells. An important feature of the CXN process is the
guarantee – all offers to buy and sell are guaranteed by a deposit. While the process
outlined above is the basic one, there are more details available in Section 6, the
Appendix, including what happens if the buyer backs out of a deal or the seller cannot
deliver as promised.

CXN makes its money from new member registration fees, from offer posting fees paid
by sellers, and from advertising.4 The buyer’s lock-in option money goes to the seller
upon successful completion of the sale. Before the offering price of a piece of
merchandise is made available to buyers, however, it requires a live, valid offer posting
certificate. Since sellers are not charged for offer posting certificates until a buyer locks
the item in, there is no need to worry about expiration dates on sellers’ offer posting
certificates.

3    Designing the Exchange Environment

Together, we reviewed the design of the exchange environment. The objective was to
design an environment in which different sellers would compete with each other through
an auction mechanism. The competition between the sellers would yield the buyers the
most competitive price for each piece of merchandise. Sellers would gain access to a
much larger market than was available locally, and make up in volume of sales what may
be lost in reduction of gross profit per unit sold. Buyers would save time and money
looking for the best available deal.

To fulfill its objective, the environment should:
        1. Guarantee each buyer would receive the lowest possible price available on
             CXN at that point in time
        2. Guarantee the lowest-cost seller on CXN at each point in time would receive
             the sale, hence ensuring efficient trades in the economic definition of the word
        3. Take advantage of the dynamic, interactive nature of the Internet
        4. Encourage many different sellers to join CXN

Assumptions made about the environment and participants were as follows:
     1. Each buyer who decides to buy will take the lowest price offered at that
         instant in time. Hence, while there may be several buyers over the course of a



4
  Although small at first, advertising revenue will rise as the site gains popularity. Initially, there is no
revenue from advertising; once it is fully operational, the company expects the advertising revenue will
contribute substantially to total revenue.


                                                        3
business day, at any given instant the multiple sellers are competing for the
              business of a single buyer. 5
         2.   A single auction begins immediately after one sale is made, and runs
              continuously until the next sale is made. Many successive auctions may be
              run over a given period of time.
         3.   Each buyer who buys will purchase one item at a time. The sale of two items
              to the same buyer will be modeled as two successive sales of one item.
         4.   The bidders (here, the sellers) operate on an independent private values
              model. Each seller has complete, private knowledge about his own
              (independent) cost to offer the product.6
         5.   The purpose of the exchange environment is to employ a mechanism which
              will encourage the sellers to truthfully reveal the lowest price at which they
              will offer the items.7
         6.   The sellers are risk-neutral.
         7.   The total sale price is a function of the bids alone; there are no contingent
              payments or additional deals (outside of the lock-in option fee and the offer
              posting certificate price).
         8.   It is both an interactive and a dynamic exchange environment.


3.1    Starting with the Traditional English Auction

The first decision was which type of auction to use. There are four major types of
auctions in the literature: the English auction, the Dutch auction, the first-price sealed-
bid auction, and the Vickrey auction. While space does not allow a comprehensive
overview here, for an excellent overview and explanation of these four types of auctions,
see Milgrom [8], Smith [10], Vickrey [11], or McAfee and McMillan [7]. For a more
theoretical analysis of the auction environment, see Milgrom and Weber’s paper [9], and
for a more mathematical analysis of auction strategy, see Wilson [12].

CXN had decided to offer the items using a type of English auction; this section draws
upon auction theory literature to explain how and why the English auction is a good fit
for the CXN environment. The English auction tends to lead to lower selling prices in
this case, and offers opportunities to use the information technology in new, unique ways.
5
  While each individual sale is made to an individual buyer, it is the collective purchasing power of many
buyers which will encourage the sellers to join CXN.
6
  Loosely, an independent private values model says all bidders value the item being sold differently and
independently. The alternative, the common values model, says the value of the item depends not only on
the individual bidder’s private information, but also upon some external factor. A typical common values
model applies when the item being sold is an oil field, in which case the common value, the (unknown)
amount of oil available, has an effect on the bidders. Because there is not an unknown value of winning the
contract, but rather each seller has his own known, private cost, the independent private values model
applies (see McAfee and McMillan [7, p. 705] for more on why the independent private values model
applies here; for a more comprehensive explanation, see Milgrom’s excellent primer [8]).
7
  In practice, the exchange environment here will have all sellers except the lowest bidder truthfully reveal
their reservation prices. The lowest priced seller only needs to beat the second-lowest-priced seller. This
dynamic is exactly parallel to the English oral ascending auction, in which the winner wins the item at the
reservation price of the second-highest bidder.


                                                     4
The traditional English auction is an open outcry, oral, ascending-bid auction which
begins with all bidders in the same place at the same time, and ends (usually a short while
later) when only one bidder is left. While the auction is ongoing, each bidder may
continuously update her bid, and can do so with knowledge of the current bids of the
other bidders. The English auction sells a single indivisible object to one of many
bidders, and assigns the object to the bidder who values the object most highly8 at the
price of the second-highest valuation. To this we would add McAfee and McMillan’s
“benchmark” auction assumptions [7, p. 706] which state that bidders are risk neutral,
hold independent private values assumptions, are symmetric, and that payment is a
function of the bids alone.9 (Although traditional English auctions are between a single
seller and many buyers, and CXN’s auction is between a single buyer and many sellers,
the dynamics are theoretically the same. The reversal is valid.)

The English auction tends to yield a more favorable average sale price. In an ascending
auction, the traditional English auction yields a higher average sale price than the Vickrey
auction, which in turn yields a higher average price than either the Dutch or first-price
sealed-bid auction [9, p. 1095]. This result holds whether the auction is ascending (in a
traditional English auction) or descending (like CXN’s), and so the English auction is an
excellent way to achieve the goal of offering buyers the lowest possible price.

Additionally, the English auction has a dynamic element to it which is not present in
sealed-bid auctions. Information technology can be used to exploit this dynamic element,
expanding the traditional English auction along the time dimension. This also makes the
English auction a good fit for CXN’s purposes.


3.2      Departing from the English Auction: Major Differences

The English auction provided a good starting place. The next task was to take advantage
of the Internet’s special characteristics to further design the sales mechanism. The largest
departure from traditional auction theory comes in the time element. The Internet frees
the auctioneer from fixed starting and ending times, and instead allows the auction to run
continuously over time. As stated above, a new auction begins immediately after
purchase of the last item, and ends each time the buyer purchases an item. Sellers cannot
determine when this will be.

In the traditional English auction, all bidders must participate simultaneously. A bidder’s
best strategy is generally to remain active until the price exceeds her threshold, at which
time she drops out. Harstad and Rothkopf [5] show that even if dropping out and re-entry
is allowed in an English auction, the bidder gains nothing by doing so. The Internet
technology changes the basic assumption that all bidders participate simultaneously.
Instead, it allows bidders to participate asynchronously, and to “drop in” and “drop out”
of auctions by viewing the auction on a Web browser. It was decided that CXN would
8
    And hence, the English auction is economically efficient.
9
    This assumes that no post-sale incentive payments are used.


                                                      5
design its sellers’ bidding screens to allow each seller to view the best current bids on a
piece of merchandise, and also to view which of those bids are hers. She has the option
to place a new bid, or to revise existing bids.10

A second difference between the traditional English auction and the Internet-enabled
auction is the time dimension. In the English auction, a single auctioneer auctions the
item – in CXN’s case, it would be the exchange network auctioning off the right to sell a
single unit to a single buyer. There would be no value in placing the second place bid.
However, the time dimension of the Internet-based auction means that new bidders (and
hence more competition for the sellers) could potentially arrive any minute. Moreover,
new buyers can arrive at any time. While each buyer would naturally take the lowest
possible price offered, if the inventory at the extremely low price were exhausted, the
“second place” bidder would gain the sale. Hence, in the CXN auction, there can be
great value in being at second, third, etc. place in the sales “pecking order” for the
continuous auction. The seller screens were designed so each seller could see the
positioning of all bids.

A third difference between the traditional English auction and the CXN exchange auction
is how they each handle multiple item auctions. The literature on English auctions
includes papers on multiple items (see [1-4, 6]). When the items are identical, a
traditional English auction (or a Vickrey auction – see [11, p. 24]) will sell the N identical
items to the N highest bidders at the N+1th highest price. Bidders will have no incentive
to bid further, given they have won some item and all items are identical. However, the
auctioneer would ideally like to extract the surplus from each possible bidder – in CXN’s
case, the consumers would like to encourage each seller to go as low as possible in price.

CXN solves this issue by breaking the multiple item auction into successive single
buyers, purchasing a single item at a time. CXN allows sellers to place bids to sell
multiple identical items at a given price or at different prices. The winner of the sale is
the seller who has the lowest price at the moment the next individual buyer decides to
make the purchase. The sellers here do not know how many buyers will arrive during the
course of a day, and hence there is not the security of knowing one is in the top N bidders
for N items. Each seller has an incentive to be the low-price seller to ensure winning the
next sale.


3.3    Supporting a New Auction with Information Technology

In addition to supporting the dynamic continuous-time element to the auction, the
Internet has several characteristics which make it a unique and powerful tool. It has
global reach and can handle asynchronous transactions. It has a broad audience, and can


10
  The seller can revise existing bids subject to the following restrictions. A new bid must remain up for at
least 24 hours, and in the initial 24 hours, the seller cannot change the bid to a higher price, nor can the
seller cancel the bid in its initial 24 hours. These restrictions apply both to new bids and to newly lowered
bids.


                                                      6
transmit data quite inexpensively. Additionally, Web browsers and other graphical user
interfaces make it relatively easy to use.

These capabilities will benefit CXN in three major ways. First, the Internet will bring in
a larger number of sellers. Second, the Internet will help CXN to run a continuous,
asynchronous auction mechanism. Third, English auctions are often susceptible to rings
of bidders, and the anonymity chosen by CXN and allowed by the Internet should reduce
that likelihood.

The Internet is useful to bring in a larger number of potential bidders than could
realistically be assembled in single place for the sale. Since it allows any seller to join
and offer merchandise at any time, the Internet also lends a bit of uncertainty to the exact
number of sellers competing at any one time. Furthermore, the ease of use of most Web
browsers, and the general connectivity of the Internet will allow many sellers, even those
not very technologically advanced, to participate in CXN relatively easily. In general,
with auctions, raising the number of bidders yields a more favorable price for the
auctioneer [7, p. 729]; the hope is the Internet will bring in a large number of sellers and
give the buyers extremely favorable pricing.

Second, the Internet will help CXN run a continuous, asynchronous auction. By
accepting bids from sellers at any time of day, and allowing buyers to take advantage of
these offers around the clock, CXN will be able to continuously update the exchange
prices, again making it simple for consumers to buy items here.

Third, traditional English auctions are susceptible to rings of colluding bidders [8, p. 18].
In such a ring, the bidders agree to elect one member of the ring to participate in the
English auction, bidding up to the ring’s (highest) reservation price; if the item is won,
the members re-auction the item among themselves. The capability made possible by the
Internet will prevent such types of rings from forming, because the bidders (sellers) do
not know each others’ identity. Only seller quantities and prices are revealed, hence
making collusion nearly impossible.


3.4   Comparing the Traditional English Auction and CXN

Figure 2 summarizes the similarities and differences between the CXN auction and a
traditional English auction:




                                              7
Figure 2 Comparison between traditional English auction and CXN
    Similarities
       Traditional English auction and CXN
       One auctioneer, several bidders
       Single, indivisible unit for sale
       Independent private values model for bidders
       Bidding level and number of active bidders continuously displayed while auction is
           ongoing
       Bidders assumed risk-neutral

    Differences
        Traditional English auction                CXN
        Auction has distinct beginning and end     Auction is continuous; bidders may “drop
                                                     in” and “drop out” at will
       Known number of bidders in each             Number of bidders is unknown and
          auction                                    potentially quite large
       No value in being runner-up                 Potential large value in being second- or
                                                     third-place bid, for when winner sells
                                                     out of inventory
       Bidders typically know less about true      Bidders typically know more about true
          value of item than does auctioneer         value of item than does auctioneer
       Vulnerable to rings of bidders              Less vulnerable to rings of bidders




4    Value Added from the Information System

The information systems capability provides CXN with the opportunity to add more
value for sellers also. In addition to reducing the selling costs and allowing access to a
larger market of consumers, CXN can offer information technology capabilities. A few
are detailed here.

After a buyer has purchased an option to lock in the offering price offered by a given
seller, that particular offer posting certificate is considered used. To offer another piece
of merchandise to another buyer, the seller needs a new offer posting certificate. CXN
offers its sellers the ability to automatically renew their offer posting certificates upon the
sale of a piece of merchandise. This allows the seller to purchase a new offer posting
certificate to keep the rest of the offers “live” and visible to buyers.

CXN offers a “My Office” feature which allows a seller to view her own current offers to
sell and the status of current transactions.




                                               8
5   Conclusions and Areas for Further Research

CXN presents an interesting preliminary case study. It plans to provide an online auction
environment which will change the way consumer goods are bought and sold. It offers
guaranteed transaction services, so that each offer to buy or sell must be guaranteed by a
small deposit which is forfeited if the transaction is not carried out as planned. It reverses
the traditional English auction, offering instead an auction which has sellers compete to
offer buyers the lowest price.

This is only a preliminary case study writeup. Many further research and practical
business issues remain, and many can only be addressed once CXN is up and working.
The actual dynamics of bidding and seller strategy will be interesting and informative.
How do sellers bid? Do they follow the independent private values model? Is there
affiliation between seller offers? What is the seller’s optimal strategy? The other side of
the coin will prove interesting as well. What is the bidder arrival process? Can it be
modeled as a Poisson process, or is some other stochastic model more appropriate? CXN
is in a unique place to capture such dynamic information about the bidding and sales
process because of its electronic commerce systems and databases.

The practical business side of the case study is also of interest. Is CXN viable? Will
consumers actually buy products online instead of choosing to go to local, more
expensive stores? Will sellers actually choose to offer products online, or will they opt to
remain in local businesses? Will warehouses, importers, or other middlemen become
involved?

It will be quite interesting to see what the outcome of this startup business venture will
be.




                                              9
6    Appendix

The appendix details the workings of the buy and sell certificates for participants on the
exchange. The most important concept is that offers to buy and sell on CXN are
guaranteed by a deposit.

Variables:
        $c     price of offer posting certificate bought by seller. This depends on the
price of the merchandise offered, and is not determined until the merchandise is actually
sold.
        $p     the seller’s bid price for the merchandise
        $g     the seller’s guarantee
        $L     fee of buyer’s lock-in option

The sequence of events is as follows, and assumes the buyer and seller have already
joined CXN by paying the one-time new membership fee. Additionally, the seller has set
up the appropriate accounts with CXN.


Table 1 outlines the money which has changed hands so far:


                 Table 1 Initial Sequence of Transactions
Description                                 Seller     CXN                            Buyer
1. The seller offers the item for sale
2. The buyer sees the item and decides to
   purchase it.
3. The buyer purchases a lock-in option                 +L                              -L
   from CXN for $L.
4. The seller gives CXN a (refundable)        -g        +g
   guarantee of sale $g.
5. CXN gives the buyer the seller’s
   information and the buyer contacts the
   seller.11
TOTAL                                         –g       g +L                             -L




11
  The buyer should contact the seller within 24 hours of receiving the seller information. Within 24 hours
of being contacted by the buyer, the seller should provide evidence of delivery (either physical delivery if
local, or a shipping number if not.)


                                                     10
At this point, the transaction will proceed in one of three ways:
        A. The seller can deliver the merchandise and the buyer pays (shown in Table 2)
        B. The seller cannot deliver the merchandise (shown in Table 3)
        C. The buyer changes his mind and decides not to exercise his option to buy
            (shown in Table 4)


A. The seller can deliver the merchandise and the buyer pays


                  Table 2 Seller and Buyer Agree to Close Sale
Description                                               Seller        CXN           Buyer
TOTAL after Step 5 above:                                  -g           g+L            -L
1. The buyer pays the purchase fee to the                  +p                          -p
   seller, usually by credit card over the
   telephone
2. The seller delivers the merchandise to                 -Item                       +Item
   the buyer

3. CXN refunds the seller’s guarantee                      +g             -g
   money
4. The seller is charged the offer posting                  -c            +c
   certificate fee (determined by sale
   price p)
5. CXN gives the buyer’s lock-in option                    +L             -L
   money to the seller.12


TOTAL                                                   (L-c) +           +c        Item – L
                                                       (p-Item)                        -p




12
   The buyer’s lock-in money is transferred to the seller one business week (five business days) after the
initial purchase by the buyer. CXN holds the money for those five days.


                                                     11
B. The seller cannot deliver the merchandise




           Table 3 The Seller Cannot Deliver the Merchandise
Description                                      Seller   CXN          Buyer
TOTAL after Step 5 above:                         -g      g+L           -L
   6. The seller is unable to deliver the
       merchandise to the buyer
   7. CXN forwards the seller’s                            -g           +g
       guarantee money to the buyer
   8. CXN refunds the buyer’s lock-in                      -L           +L
       option money to the buyer


TOTAL                                             –g                    +g



C. The buyer changes his mind and forfeits the lock-in option money.


                 Table 4 The Buyer Changes His Mind
Description                             Seller     CXN                 Buyer
TOTAL after Step 5 above:                 -g       g+L                  -L
   5. CXN forwards the buyer’s lock-in   +L         -L
       option money to the seller

   6. CXN refunds the seller’s                    +g       -g
      guarantee money to the seller

TOTAL                                              L                    -L




                                            12
References


[1]    Beam, Carrie, “Auctions on the Internet: An Application of Operations Research
       to Electronic Commerce,” Department of Industrial Engineering and Operations
       Research, University of California, Berkeley, Berkeley, CA Qualifying
       examination, November 11 1996.
[2]    Burns, Penny, “Market Structure and Buyer Behaviour: Price Adjustment in a
       Multi-Object Progressive Oral Auction,” Journal of Economic Behavior &
       Organization, vol. 6, pp. 275-300, 1985.
[3]    Demange, Gabrielle, David Gale, and Marilda Sotomayor, “Multi-Item
       Auctions,” Journal of Political Economy, vol. 94, pp. 863-872, 1986.
[4]    Engelbrecht-Wiggans, Richard and Robert J. Weber, “An Example of a Multi-
       Object Auction Game,” Management Science, vol. 25, pp. 1272-1276, 1979.
[5]    Harstad, Ronald M. and Michael H. Rothkopf, “An Alternating Recognition
       Model of English Auctions,” Rutgers University, New Brunswick, NJ
       Unpublished working paper, February 1994.
[6]    Hausch, Donald B., Michael H. Rothkopf, Elmer Dougherty, and Marshall Rose,
       “Multi-Object Auctions: Sequential vs. Simultaneous Sales/Comment,”
       Management Science, vol. 32, pp. 1599-1612, 1986.
[7]    McAfee, R. Preston and John McMillan, “Auctions and Bidding,” Journal of
       Economic Literature, vol. 25, pp. 699-738, 1987.
[8]    Milgrom, P., “Auctions and Bidding - a Primer,” Journal of Economic
       Perspectives, vol. 3, pp. 3-22, 1989.
[9]    Milgrom, Paul R. and Robert J. Weber, “A Theory of Auctions and Competitive
       Bidding,” Econometrica, vol. 50, pp. 1089-1122, 1982.
[10]   Smith, Vernon L., “Auctions,” in The New Palgrave: A Dictionary of Economics,
       vol. 1, J. Eatwell, M. Milgate, and P. Newman, Eds. New York, NY: The
       Stockton Press, 1987, pp. 138-144.
[11]   Vickrey, William, “Counterspeculation, Auctions, and Competitive Sealed
       Tenders,” Journal of Finance, vol. March, pp. 8-37, 1961.
[12]   Wilson, Robert, “Chapter 8: Strategic Analysis of Auctions,” in Handbook of
       game theory with economic applications, R. J. Aumann and S. Hart, Eds. New
       York, NY: North-Holland, 1992.




                                         13

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Cxn, A Case Study

  • 1. CXN: A Case Study Carrie Beam Gene Fusz The Fisher Center for Management, President, CXN Information and Technology 925 N. Lindbergh Blvd Haas School of Business St. Louis, MO 63141 University of California, Berkeley genefusz@cxn.com Berkeley, CA 94720 beam@haas.berkeley.edu CMIT Working Paper 97-WP-1025 October 14, 1997
  • 2. Table of Contents 1 Introduction............................................................................................................. 1 2 Background ............................................................................................................. 1 3 Designing the Exchange Environment ..................................................................... 3 3.1 Starting with the Traditional English Auction ...................................................... 4 3.2 Departing from the English Auction: Major Differences ..................................... 5 3.3 Supporting a New Auction with Information Technology .................................... 6 3.4 Comparing the Traditional English Auction and CXN ......................................... 7 4 Value Added from the Information System.............................................................. 8 5 Conclusions and Areas for Further Research............................................................ 9 6 Appendix............................................................................................................... 10 List of Tables Table 1 Initial Sequence of Transactions ...................................................................... 10 Table 2 Seller and Buyer Agree to Close Sale............................................................... 11 Table 3 The Seller Cannot Deliver the Merchandise ..................................................... 12 Table 4 The Buyer Changes His Mind.......................................................................... 12
  • 3. Abstract CXN is a startup company which is designing an Internet-based exchange mechanism to sell new consumer products (such as televisions) in a new and efficient manner. It introduces a variant of the standard English auction, in which sellers are the bidders and the single buyer is the auctioneer. CXN uses information technology and the Internet to depart from standard English auction methodology. Major differences include the support of asynchronous bidder participation, the continuously running auction, and the ability to auction off multiple items in a succession of single-item sales. Additionally, the Internet provides a broader audience and grants some degree of immunity from rings of bidders. 1 Introduction This case study outlines the workings of the Consumer Exchange Network, or CXN (www.cxn.com). CXN is a St. Louis, MO-based startup company with the mission of providing an efficient online pricing mechanism to bring together buyers and sellers of new consumer products. Gene Fusz, the President of CXN, called Carrie Beam of the Fisher Center in the spring of 1997 to discuss the workings of the new business. This case study has come out of the collaboration between Gene and Carrie. CXN is currently in beta testing. The site offers camcorders only at this point in time, and is looking for further funding before it broadens its offerings. 2 Background CXN grew out of a desire to bring buyers and sellers of new branded consumer products, such as televisions and VCRs, together in an efficient manner. Consumer products are sold on the “Big Board.” CXN is an Internet-based exchange environment which sells new consumer products through a patent-pending auction mechanism. Because it provides no warehousing, transportation, or advertising, it hopes to provide buyers with a more efficient and less expensive environment than the traditional consumer products superstores, such as Fry’s Electronics or Best Buy. While business-to-business procurement is certainly not excluded, CXN currently targets individual buyers and attempts to match them with corporate sellers. The corporate sellers could include (but are not limited to) current superstores, importers, and warehouses. Briefly, this is how CXN works. Both buyers and sellers are anonymous until a sale has been made, at which time CXN provides the parties the information necessary to complete the sale. 1
  • 4. From the seller’s point of view, CXN works as follows. First, seller joins the CXN network for one-time member registration fee of $25 or less. Second, the seller purchases an offer posting certificate; the certificate details the type of merchandise offered and the offering price. The price of the certificate depends on the asking price of the merchandise being sold, and will be from $1-$10 for products costing from $50 to $1000. Third, the seller’s offer becomes visible to buyers only if it’s the lowest priced offer. If a buyer chooses to purchase the seller’s merchandise, CXN will provide each party with information necessary to contact the other, and the trade is arranged.1 From the buyer’s point of view, CXN works as follows. Buyers must first join the CXN network by paying a one-time new member registration fee of $25 or less. A buyer interested in a new color television will then locate the product on the CXN menu. The buyer will see only the lowest price offered nationwide, a price which was determined by the auction environment in which several sellers bid against each other.2 The environment was designed to make the buyer’s experience as simple and easy as possible. The buyer will then purchase an option for $10, which locks in the price for that product for one day (8 full business hours). CXN provides the buyer with information necessary to contact the seller, and the trade is arranged. A preliminary sellers’ bidding screen design is shown below in Figure 1. This screen is available only to sellers, and it shows the seller the differing price levels, as well as the quantity available at each price. Buyers only see the lowest price offered – in this case, $200 for the television. Figure 1 Preliminary Screen Design Sony 19” Color TV Quantity Available Timestamp $210 10 4/2/97 $205 42 3/25/97 $200 35 4/2/97 $200 4 4/1/97 3 $195 1 To protect buyer privacy, currently CXN provides the buyer’s name and email address only to the seller. In addition to the seller’s name and email address, the buyer receives the seller’s telephone number, fax number, company name and address, contact person, and, where appropriate, driving directions. 2 Currently, shipping costs are not included. They average $10-$20 on a several-hundred-dollar camcorder. CXN plans to have ZIP code functionality which determines buyer and seller locations and then adds appropriate shipping costs to the price each buyer sees. Hence, the price an individual buyer sees is the lowest price, including shipping, available to her; it may or may not reflect the lowest raw price nationwide. This is an important part of CXN’s offerings; however, in the interests of simplicity this case study deliberately excludes the ZIP code when formulating the basic model. It assumes instead shipping and handling costs are the same from all sellers to all buyers. The offering prices on the CXN exchange do not include sales tax. 3 There is no current offer at $195; the lowest current offer is $200. The $195 is there to make it more inviting for the sellers to move down to the next level. 2
  • 5. Items are sorted (and hence offered to buyers) first by lowest price, and then by earliest timestamp. Several sellers may be at each price level; in that case, CXN relies upon slight differences in timestamp to differentiate them. Each seller may offer a single item for sale by purchasing a single offer posting certificate. Each seller may also offer an entire lot of identical items at the same price by purchasing a single offer posting certificate and choosing the automatic renew feature, to purchase another offer posting certificate when the first one sells. An important feature of the CXN process is the guarantee – all offers to buy and sell are guaranteed by a deposit. While the process outlined above is the basic one, there are more details available in Section 6, the Appendix, including what happens if the buyer backs out of a deal or the seller cannot deliver as promised. CXN makes its money from new member registration fees, from offer posting fees paid by sellers, and from advertising.4 The buyer’s lock-in option money goes to the seller upon successful completion of the sale. Before the offering price of a piece of merchandise is made available to buyers, however, it requires a live, valid offer posting certificate. Since sellers are not charged for offer posting certificates until a buyer locks the item in, there is no need to worry about expiration dates on sellers’ offer posting certificates. 3 Designing the Exchange Environment Together, we reviewed the design of the exchange environment. The objective was to design an environment in which different sellers would compete with each other through an auction mechanism. The competition between the sellers would yield the buyers the most competitive price for each piece of merchandise. Sellers would gain access to a much larger market than was available locally, and make up in volume of sales what may be lost in reduction of gross profit per unit sold. Buyers would save time and money looking for the best available deal. To fulfill its objective, the environment should: 1. Guarantee each buyer would receive the lowest possible price available on CXN at that point in time 2. Guarantee the lowest-cost seller on CXN at each point in time would receive the sale, hence ensuring efficient trades in the economic definition of the word 3. Take advantage of the dynamic, interactive nature of the Internet 4. Encourage many different sellers to join CXN Assumptions made about the environment and participants were as follows: 1. Each buyer who decides to buy will take the lowest price offered at that instant in time. Hence, while there may be several buyers over the course of a 4 Although small at first, advertising revenue will rise as the site gains popularity. Initially, there is no revenue from advertising; once it is fully operational, the company expects the advertising revenue will contribute substantially to total revenue. 3
  • 6. business day, at any given instant the multiple sellers are competing for the business of a single buyer. 5 2. A single auction begins immediately after one sale is made, and runs continuously until the next sale is made. Many successive auctions may be run over a given period of time. 3. Each buyer who buys will purchase one item at a time. The sale of two items to the same buyer will be modeled as two successive sales of one item. 4. The bidders (here, the sellers) operate on an independent private values model. Each seller has complete, private knowledge about his own (independent) cost to offer the product.6 5. The purpose of the exchange environment is to employ a mechanism which will encourage the sellers to truthfully reveal the lowest price at which they will offer the items.7 6. The sellers are risk-neutral. 7. The total sale price is a function of the bids alone; there are no contingent payments or additional deals (outside of the lock-in option fee and the offer posting certificate price). 8. It is both an interactive and a dynamic exchange environment. 3.1 Starting with the Traditional English Auction The first decision was which type of auction to use. There are four major types of auctions in the literature: the English auction, the Dutch auction, the first-price sealed- bid auction, and the Vickrey auction. While space does not allow a comprehensive overview here, for an excellent overview and explanation of these four types of auctions, see Milgrom [8], Smith [10], Vickrey [11], or McAfee and McMillan [7]. For a more theoretical analysis of the auction environment, see Milgrom and Weber’s paper [9], and for a more mathematical analysis of auction strategy, see Wilson [12]. CXN had decided to offer the items using a type of English auction; this section draws upon auction theory literature to explain how and why the English auction is a good fit for the CXN environment. The English auction tends to lead to lower selling prices in this case, and offers opportunities to use the information technology in new, unique ways. 5 While each individual sale is made to an individual buyer, it is the collective purchasing power of many buyers which will encourage the sellers to join CXN. 6 Loosely, an independent private values model says all bidders value the item being sold differently and independently. The alternative, the common values model, says the value of the item depends not only on the individual bidder’s private information, but also upon some external factor. A typical common values model applies when the item being sold is an oil field, in which case the common value, the (unknown) amount of oil available, has an effect on the bidders. Because there is not an unknown value of winning the contract, but rather each seller has his own known, private cost, the independent private values model applies (see McAfee and McMillan [7, p. 705] for more on why the independent private values model applies here; for a more comprehensive explanation, see Milgrom’s excellent primer [8]). 7 In practice, the exchange environment here will have all sellers except the lowest bidder truthfully reveal their reservation prices. The lowest priced seller only needs to beat the second-lowest-priced seller. This dynamic is exactly parallel to the English oral ascending auction, in which the winner wins the item at the reservation price of the second-highest bidder. 4
  • 7. The traditional English auction is an open outcry, oral, ascending-bid auction which begins with all bidders in the same place at the same time, and ends (usually a short while later) when only one bidder is left. While the auction is ongoing, each bidder may continuously update her bid, and can do so with knowledge of the current bids of the other bidders. The English auction sells a single indivisible object to one of many bidders, and assigns the object to the bidder who values the object most highly8 at the price of the second-highest valuation. To this we would add McAfee and McMillan’s “benchmark” auction assumptions [7, p. 706] which state that bidders are risk neutral, hold independent private values assumptions, are symmetric, and that payment is a function of the bids alone.9 (Although traditional English auctions are between a single seller and many buyers, and CXN’s auction is between a single buyer and many sellers, the dynamics are theoretically the same. The reversal is valid.) The English auction tends to yield a more favorable average sale price. In an ascending auction, the traditional English auction yields a higher average sale price than the Vickrey auction, which in turn yields a higher average price than either the Dutch or first-price sealed-bid auction [9, p. 1095]. This result holds whether the auction is ascending (in a traditional English auction) or descending (like CXN’s), and so the English auction is an excellent way to achieve the goal of offering buyers the lowest possible price. Additionally, the English auction has a dynamic element to it which is not present in sealed-bid auctions. Information technology can be used to exploit this dynamic element, expanding the traditional English auction along the time dimension. This also makes the English auction a good fit for CXN’s purposes. 3.2 Departing from the English Auction: Major Differences The English auction provided a good starting place. The next task was to take advantage of the Internet’s special characteristics to further design the sales mechanism. The largest departure from traditional auction theory comes in the time element. The Internet frees the auctioneer from fixed starting and ending times, and instead allows the auction to run continuously over time. As stated above, a new auction begins immediately after purchase of the last item, and ends each time the buyer purchases an item. Sellers cannot determine when this will be. In the traditional English auction, all bidders must participate simultaneously. A bidder’s best strategy is generally to remain active until the price exceeds her threshold, at which time she drops out. Harstad and Rothkopf [5] show that even if dropping out and re-entry is allowed in an English auction, the bidder gains nothing by doing so. The Internet technology changes the basic assumption that all bidders participate simultaneously. Instead, it allows bidders to participate asynchronously, and to “drop in” and “drop out” of auctions by viewing the auction on a Web browser. It was decided that CXN would 8 And hence, the English auction is economically efficient. 9 This assumes that no post-sale incentive payments are used. 5
  • 8. design its sellers’ bidding screens to allow each seller to view the best current bids on a piece of merchandise, and also to view which of those bids are hers. She has the option to place a new bid, or to revise existing bids.10 A second difference between the traditional English auction and the Internet-enabled auction is the time dimension. In the English auction, a single auctioneer auctions the item – in CXN’s case, it would be the exchange network auctioning off the right to sell a single unit to a single buyer. There would be no value in placing the second place bid. However, the time dimension of the Internet-based auction means that new bidders (and hence more competition for the sellers) could potentially arrive any minute. Moreover, new buyers can arrive at any time. While each buyer would naturally take the lowest possible price offered, if the inventory at the extremely low price were exhausted, the “second place” bidder would gain the sale. Hence, in the CXN auction, there can be great value in being at second, third, etc. place in the sales “pecking order” for the continuous auction. The seller screens were designed so each seller could see the positioning of all bids. A third difference between the traditional English auction and the CXN exchange auction is how they each handle multiple item auctions. The literature on English auctions includes papers on multiple items (see [1-4, 6]). When the items are identical, a traditional English auction (or a Vickrey auction – see [11, p. 24]) will sell the N identical items to the N highest bidders at the N+1th highest price. Bidders will have no incentive to bid further, given they have won some item and all items are identical. However, the auctioneer would ideally like to extract the surplus from each possible bidder – in CXN’s case, the consumers would like to encourage each seller to go as low as possible in price. CXN solves this issue by breaking the multiple item auction into successive single buyers, purchasing a single item at a time. CXN allows sellers to place bids to sell multiple identical items at a given price or at different prices. The winner of the sale is the seller who has the lowest price at the moment the next individual buyer decides to make the purchase. The sellers here do not know how many buyers will arrive during the course of a day, and hence there is not the security of knowing one is in the top N bidders for N items. Each seller has an incentive to be the low-price seller to ensure winning the next sale. 3.3 Supporting a New Auction with Information Technology In addition to supporting the dynamic continuous-time element to the auction, the Internet has several characteristics which make it a unique and powerful tool. It has global reach and can handle asynchronous transactions. It has a broad audience, and can 10 The seller can revise existing bids subject to the following restrictions. A new bid must remain up for at least 24 hours, and in the initial 24 hours, the seller cannot change the bid to a higher price, nor can the seller cancel the bid in its initial 24 hours. These restrictions apply both to new bids and to newly lowered bids. 6
  • 9. transmit data quite inexpensively. Additionally, Web browsers and other graphical user interfaces make it relatively easy to use. These capabilities will benefit CXN in three major ways. First, the Internet will bring in a larger number of sellers. Second, the Internet will help CXN to run a continuous, asynchronous auction mechanism. Third, English auctions are often susceptible to rings of bidders, and the anonymity chosen by CXN and allowed by the Internet should reduce that likelihood. The Internet is useful to bring in a larger number of potential bidders than could realistically be assembled in single place for the sale. Since it allows any seller to join and offer merchandise at any time, the Internet also lends a bit of uncertainty to the exact number of sellers competing at any one time. Furthermore, the ease of use of most Web browsers, and the general connectivity of the Internet will allow many sellers, even those not very technologically advanced, to participate in CXN relatively easily. In general, with auctions, raising the number of bidders yields a more favorable price for the auctioneer [7, p. 729]; the hope is the Internet will bring in a large number of sellers and give the buyers extremely favorable pricing. Second, the Internet will help CXN run a continuous, asynchronous auction. By accepting bids from sellers at any time of day, and allowing buyers to take advantage of these offers around the clock, CXN will be able to continuously update the exchange prices, again making it simple for consumers to buy items here. Third, traditional English auctions are susceptible to rings of colluding bidders [8, p. 18]. In such a ring, the bidders agree to elect one member of the ring to participate in the English auction, bidding up to the ring’s (highest) reservation price; if the item is won, the members re-auction the item among themselves. The capability made possible by the Internet will prevent such types of rings from forming, because the bidders (sellers) do not know each others’ identity. Only seller quantities and prices are revealed, hence making collusion nearly impossible. 3.4 Comparing the Traditional English Auction and CXN Figure 2 summarizes the similarities and differences between the CXN auction and a traditional English auction: 7
  • 10. Figure 2 Comparison between traditional English auction and CXN Similarities Traditional English auction and CXN One auctioneer, several bidders Single, indivisible unit for sale Independent private values model for bidders Bidding level and number of active bidders continuously displayed while auction is ongoing Bidders assumed risk-neutral Differences Traditional English auction CXN Auction has distinct beginning and end Auction is continuous; bidders may “drop in” and “drop out” at will Known number of bidders in each Number of bidders is unknown and auction potentially quite large No value in being runner-up Potential large value in being second- or third-place bid, for when winner sells out of inventory Bidders typically know less about true Bidders typically know more about true value of item than does auctioneer value of item than does auctioneer Vulnerable to rings of bidders Less vulnerable to rings of bidders 4 Value Added from the Information System The information systems capability provides CXN with the opportunity to add more value for sellers also. In addition to reducing the selling costs and allowing access to a larger market of consumers, CXN can offer information technology capabilities. A few are detailed here. After a buyer has purchased an option to lock in the offering price offered by a given seller, that particular offer posting certificate is considered used. To offer another piece of merchandise to another buyer, the seller needs a new offer posting certificate. CXN offers its sellers the ability to automatically renew their offer posting certificates upon the sale of a piece of merchandise. This allows the seller to purchase a new offer posting certificate to keep the rest of the offers “live” and visible to buyers. CXN offers a “My Office” feature which allows a seller to view her own current offers to sell and the status of current transactions. 8
  • 11. 5 Conclusions and Areas for Further Research CXN presents an interesting preliminary case study. It plans to provide an online auction environment which will change the way consumer goods are bought and sold. It offers guaranteed transaction services, so that each offer to buy or sell must be guaranteed by a small deposit which is forfeited if the transaction is not carried out as planned. It reverses the traditional English auction, offering instead an auction which has sellers compete to offer buyers the lowest price. This is only a preliminary case study writeup. Many further research and practical business issues remain, and many can only be addressed once CXN is up and working. The actual dynamics of bidding and seller strategy will be interesting and informative. How do sellers bid? Do they follow the independent private values model? Is there affiliation between seller offers? What is the seller’s optimal strategy? The other side of the coin will prove interesting as well. What is the bidder arrival process? Can it be modeled as a Poisson process, or is some other stochastic model more appropriate? CXN is in a unique place to capture such dynamic information about the bidding and sales process because of its electronic commerce systems and databases. The practical business side of the case study is also of interest. Is CXN viable? Will consumers actually buy products online instead of choosing to go to local, more expensive stores? Will sellers actually choose to offer products online, or will they opt to remain in local businesses? Will warehouses, importers, or other middlemen become involved? It will be quite interesting to see what the outcome of this startup business venture will be. 9
  • 12. 6 Appendix The appendix details the workings of the buy and sell certificates for participants on the exchange. The most important concept is that offers to buy and sell on CXN are guaranteed by a deposit. Variables: $c price of offer posting certificate bought by seller. This depends on the price of the merchandise offered, and is not determined until the merchandise is actually sold. $p the seller’s bid price for the merchandise $g the seller’s guarantee $L fee of buyer’s lock-in option The sequence of events is as follows, and assumes the buyer and seller have already joined CXN by paying the one-time new membership fee. Additionally, the seller has set up the appropriate accounts with CXN. Table 1 outlines the money which has changed hands so far: Table 1 Initial Sequence of Transactions Description Seller CXN Buyer 1. The seller offers the item for sale 2. The buyer sees the item and decides to purchase it. 3. The buyer purchases a lock-in option +L -L from CXN for $L. 4. The seller gives CXN a (refundable) -g +g guarantee of sale $g. 5. CXN gives the buyer the seller’s information and the buyer contacts the seller.11 TOTAL –g g +L -L 11 The buyer should contact the seller within 24 hours of receiving the seller information. Within 24 hours of being contacted by the buyer, the seller should provide evidence of delivery (either physical delivery if local, or a shipping number if not.) 10
  • 13. At this point, the transaction will proceed in one of three ways: A. The seller can deliver the merchandise and the buyer pays (shown in Table 2) B. The seller cannot deliver the merchandise (shown in Table 3) C. The buyer changes his mind and decides not to exercise his option to buy (shown in Table 4) A. The seller can deliver the merchandise and the buyer pays Table 2 Seller and Buyer Agree to Close Sale Description Seller CXN Buyer TOTAL after Step 5 above: -g g+L -L 1. The buyer pays the purchase fee to the +p -p seller, usually by credit card over the telephone 2. The seller delivers the merchandise to -Item +Item the buyer 3. CXN refunds the seller’s guarantee +g -g money 4. The seller is charged the offer posting -c +c certificate fee (determined by sale price p) 5. CXN gives the buyer’s lock-in option +L -L money to the seller.12 TOTAL (L-c) + +c Item – L (p-Item) -p 12 The buyer’s lock-in money is transferred to the seller one business week (five business days) after the initial purchase by the buyer. CXN holds the money for those five days. 11
  • 14. B. The seller cannot deliver the merchandise Table 3 The Seller Cannot Deliver the Merchandise Description Seller CXN Buyer TOTAL after Step 5 above: -g g+L -L 6. The seller is unable to deliver the merchandise to the buyer 7. CXN forwards the seller’s -g +g guarantee money to the buyer 8. CXN refunds the buyer’s lock-in -L +L option money to the buyer TOTAL –g +g C. The buyer changes his mind and forfeits the lock-in option money. Table 4 The Buyer Changes His Mind Description Seller CXN Buyer TOTAL after Step 5 above: -g g+L -L 5. CXN forwards the buyer’s lock-in +L -L option money to the seller 6. CXN refunds the seller’s +g -g guarantee money to the seller TOTAL L -L 12
  • 15. References [1] Beam, Carrie, “Auctions on the Internet: An Application of Operations Research to Electronic Commerce,” Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, CA Qualifying examination, November 11 1996. [2] Burns, Penny, “Market Structure and Buyer Behaviour: Price Adjustment in a Multi-Object Progressive Oral Auction,” Journal of Economic Behavior & Organization, vol. 6, pp. 275-300, 1985. [3] Demange, Gabrielle, David Gale, and Marilda Sotomayor, “Multi-Item Auctions,” Journal of Political Economy, vol. 94, pp. 863-872, 1986. [4] Engelbrecht-Wiggans, Richard and Robert J. Weber, “An Example of a Multi- Object Auction Game,” Management Science, vol. 25, pp. 1272-1276, 1979. [5] Harstad, Ronald M. and Michael H. Rothkopf, “An Alternating Recognition Model of English Auctions,” Rutgers University, New Brunswick, NJ Unpublished working paper, February 1994. [6] Hausch, Donald B., Michael H. Rothkopf, Elmer Dougherty, and Marshall Rose, “Multi-Object Auctions: Sequential vs. Simultaneous Sales/Comment,” Management Science, vol. 32, pp. 1599-1612, 1986. [7] McAfee, R. Preston and John McMillan, “Auctions and Bidding,” Journal of Economic Literature, vol. 25, pp. 699-738, 1987. [8] Milgrom, P., “Auctions and Bidding - a Primer,” Journal of Economic Perspectives, vol. 3, pp. 3-22, 1989. [9] Milgrom, Paul R. and Robert J. Weber, “A Theory of Auctions and Competitive Bidding,” Econometrica, vol. 50, pp. 1089-1122, 1982. [10] Smith, Vernon L., “Auctions,” in The New Palgrave: A Dictionary of Economics, vol. 1, J. Eatwell, M. Milgate, and P. Newman, Eds. New York, NY: The Stockton Press, 1987, pp. 138-144. [11] Vickrey, William, “Counterspeculation, Auctions, and Competitive Sealed Tenders,” Journal of Finance, vol. March, pp. 8-37, 1961. [12] Wilson, Robert, “Chapter 8: Strategic Analysis of Auctions,” in Handbook of game theory with economic applications, R. J. Aumann and S. Hart, Eds. New York, NY: North-Holland, 1992. 13